3r21. ABCD is a rectangular shape and Um is the midpoint of [AB].
Express each of the next vectors regarding and
(Total 4 marks)
installment payments on your The vectors, are device vectors along the x-axis and y-axis correspondingly. The vectors = вЂ“ + and = 3 + your five are given.
(a)Find + a couple of in terms of and.
A vector has the same direction because + a couple of, and includes a magnitude of 26. (b)Find in terms of and.
(Total 4 marks)
a few. The circle shown features centre O and radius 6. is a vector, is the vector and is the vector.
(a)Verify that A, W and C lie within the circle.
(b)Find the vector.
(c)Using a proper scalar product, or otherwise, locate the cosine of position. (3)
(d)Find the area of triangle DASAR, giving your answer inside the form a, where a в€€. (4)
(Total 12 marks)
4. The quadrilateral OABC has vertices with coordinates O(0, 0), A(5, 1), B(10, 5) and C(2, 7). (a)Find the vectors and.
(b)Find the angle between the gauche of the quadrilateral OABC. (Total 4 marks)
5. Find a vector formula of the series passing through (вЂ“1, 4) and (3, вЂ“1). Give your answer in the form r = p & td, in which t в€€ R (Total 4 marks)
6. Through this question, the vector kilometers represents a displacement due east, as well as the vector kilometers a displacement due north.
Two deck hands of personnel are laying an subterranean cable within a northвЂ“south path across a desert. For 06: 00 each team sets out using their base camp which is located at the source (0, 0). One staff is in a Toyundai motor vehicle and the other in a Chryssault vehicle.
The Toyundai has velocity vector km hвЂ“1, and the Chryssault has velocity vector kilometres hвЂ“1.
(a)Find the speed of each vehicle.
(b)(i)Find the position vectors of each car at 06: 30.
(ii)Hence, or otherwise, find the space between the cars at 06: 30. (3)
(c)At this time around (06: 30) the Chryssault stops as well as its crew get started their day's work, sitting cable in a northerly way. The...